# The Minimal GUT with Inflaton and Dark Matter Unification

## TL;DR

This paper proposes a minimal non-supersymmetric flipped SU(5)×U(1)_X model unifying inflaton and dark matter as a scalar field, addressing gauge unification, proton decay, neutrino masses, baryogenesis, and vacuum stability.

## Contribution

It introduces a novel unification of inflaton and dark matter as a scalar field within a minimal flipped SU(5)×U(1)_X framework, with implications for particle physics and cosmology.

## Key findings

- Gauge coupling unification achieved with vector-like fermions.
- Proton lifetime estimated around 5×10^{35} years.
- Scalar field unifies inflaton and dark matter without axion or non-minimal gravity coupling.

## Abstract

Giving up the solutions to the fine-tuning problems, we propose the non-supersymmetric flipped $SU(5)\times U(1)_X$ model based on the minimal particle content principle, which can be constructed from the four-dimensional $SO(10)$ models, five-dimensional orbifold $SO(10)$ models, and local F-theory $SO(10)$ models. To achieve gauge coupling unification, we introduce one pair of vector-like fermions, which form complete $SU(5)\times U(1)_X$ representation. Proton lifetime is around $5\times 10^{35}$ years, neutrino masses and mixing can be explained via seesaw mechanism, baryon asymmetry can be generated via leptogenesis, and vacuum stability problem can be solved as well. In particular, we propose that inflaton and dark matter particle can be unified to a real scalar field with $Z_2$ symmetry, which is not an axion and does not have the non-minimal coupling to gravity. Such kind of scenarios can be applied to the generic scalar dark matter models. Also, we find that the vector-like particle corrections to the $B_s^0$ masses can be about 6.6%, while their corrections to the $K^0$ and $B_d^0$ masses are negligible.